Publications
PUBLISHED / ACCEPTED
Tranched graphs: consequences for topology and dynamics
Authors: Michał Kowalewski, Piotr Oprocha
Fundamenta Mathematicae 273, 1-46 • 2026
We compare quasi-graphs and generalized sin(1/x)-type continua, which are two classes of continua that generalize topological graphs and contain the Warsaw circle as a nontrivial common element. We show that neither class is a subset of the other, provide some characterizations, and present illustrative examples. We unify both approaches by considering the class of tranched graphs, compare it to concepts known from the literature, and describe how the topological structure of its elements restricts possible dynamics.
Every nondegenerate Peano continuum admits a pure mixing selfmap
Authors: Klara Karasova, Michał Kowalewski, Piotr Oprocha
Proc. Amer. Math. Soc. 154, 4389-4403 • 2026
We prove that every Peano continuum (a space that is a continuous image of [0,1]) admits a topologically mixing but not exact map. The constructed map has a dense set of periodic points.
PREPRINTS
Observable Dynamics and the Generic Coincidence of Milnor, Statistical, and Physical Attractors
Authors: Magdalena Foryś-Krawiec, Jana Hantáková, Michał Kowalewski, Piotr Oprocha
preprint arXiv:2511.09718 •
We study observable dynamics of generic continuous interval maps. We prove that, for a residual subset of C([0,1]), the global Milnor, statistical, and physical attractors coincide with the non-wandering set. Thus, for a typical interval map, the asymptotic dynamics detected by Lebesgue-almost every initial condition recovers all recurrent dynamics. The common attractor is a robust Cantor set of zero Hausdorff dimension. Moreover, every invariant probability measure has a basin of zero Lebesgue measure. We also present examples showing that, outside the generic setting, positive topological entropy may occur outside the global Milnor attractor, and the three attractors need not coincide.